×

A based-DC programming approach for planning a multisensor multizone search for a moving target. (English) Zbl 1370.90126

Le Thi, Hoai An (ed.) et al., Modelling, computation and optimization in information systems and management sciences. Proceedings of the 3rd international conference on modelling, computation and optimization in information systems and management sciences, MCO 2015, Lorraine, France, May 11–13, 2015. Part I. Cham: Springer (ISBN 978-3-319-18160-8/pbk; 978-3-319-18161-5/ebook). Advances in Intelligent Systems and Computing 359, 107-118 (2015).
Summary: In this paper, we consider a well-known problem in the general area of search theory: planning a multisensor in multizone search so as to minimize the probability of non-detection of a moving target under a given resource effort to be shared. The solution method is based on a combination of the forward-backward split technique and DC programming. Numerical experiments demonstrate the efficiency of the proposed algorithm in comparison with the existing method.
For the entire collection see [Zbl 1370.90008].

MSC:

90B40 Search theory
90C26 Nonconvex programming, global optimization
90C27 Combinatorial optimization
90C30 Nonlinear programming
65K05 Numerical mathematical programming methods
Full Text: DOI

References:

[1] de Boer, P. T.; Kroese, D. P.; Mannor, S.; Rubinstein, R. Y., A Tutorial on The Cross-Entropy Method, Annals of Operations Research, 134, 19-67 (2005) · Zbl 1075.90066 · doi:10.1007/s10479-005-5724-z
[2] Brown, S. S., Optimal search for a moving target in discrete time and space, Operations Research, 32, 5, 1107-1115 (1979) · Zbl 0562.90035
[3] Cadre, J. P.; Souris, G., Searching Tracks, IEEE Transactions on Aerospace and Electronic systems, 36, 4, 1149-1166 (2000) · doi:10.1109/7.892665
[4] Dobbie, J. M., Transfer of detection contacts to tracking contacts in surveillance, Operations Research, 14, 791-800 (1966) · doi:10.1287/opre.14.5.791
[5] Frost, J. R., Principles of search theory, part III: Probability density distributions, Response, 17, 3, 1-10 (1999)
[6] de Guenin, J., Optimum distribution of effort: an extension of the Koopman theory, Operations Research, 9, 1, 1-7 (1961) · doi:10.1287/opre.9.1.1
[7] Hohzaki, R.; Iida, K., A concave minimization problem with double layers of constraints on the total amount of resources, Journal of the Operations Research Society of Japan, 43, 1, 109-127 (2000) · Zbl 1138.90452 · doi:10.1016/S0453-4514(00)88754-2
[8] Haley, K. B.; Stone, L. D., Search Theory and Applications (1980), New York: Plenum Press, New York
[9] Koopman, B. O., Search and Screening: General Principles with Historical Applications (1980), New York: Pergamon Press, New York · Zbl 0677.90037
[10] Koopman, B. O., Search and Screening: General Principle with Historical Applications (1999), Alexandria: MORS Heritage Series, Alexandria
[11] Le Thi, H. A.; Pham Dinh, T., The DC (difference of convex functions) Programming and DCA revisited with DC models of real world nonconvex optimization problems, Annals of Operations Research, 133, 23-46 (2005) · Zbl 1116.90122 · doi:10.1007/s10479-004-5022-1
[12] Le Thi, H. A.; Nguyen, D. M.; Pham Dinh, T., A DC programming approach for planning a multisensor multizone search for a target, Submitted in Computers & Operations Research, 41, 231-239 (2014) · Zbl 1348.90347 · doi:10.1016/j.cor.2012.07.006
[13] Pham Dinh, T.; Le Thi, H. A., Convex analysis approach to DC programming: Theory, Algorithms and Applications (dedicated to Professor Hoang Tuy on the occasion of his 70th birthday), Acta Mathematica Vietnamica, 22, 289-355 (1997) · Zbl 0895.90152
[14] Pham Dinh, T.; Le Thi, H. A., DC optimization algorihms for solving the trust region subproblem, SIAM J. Optimization, 8, 476-505 (1998) · Zbl 0913.65054 · doi:10.1137/S1052623494274313
[15] Rubinstein, R. Y.; Kroese, D., The cross-entropy method: a unified approach to combinatorial optimization (2004), Berlin: Springer, Berlin · Zbl 1140.90005 · doi:10.1007/978-1-4757-4321-0
[16] Simonin, S.; Cadre, J. P.; Dambreville, F., A Hierarchical Approach for Planning a Multisensor Multizone Search for a Moving Target, Computers & Operations Research, 36, 7, 2179-2192 (2009) · Zbl 1158.90360 · doi:10.1016/j.cor.2008.08.007
[17] Stone, L.D.: Necessary and suffcient conditions for optimal search plans for moving targets. Mathematics of Operations Research (4), 431-440 (1979); Math. Sci. Net. · Zbl 0424.90036
[18] Stone, L. D., What’s happened in search theory since the 1975 Lanchester prize?, Operations Research, 37, 3, 501-506 (1989) · doi:10.1287/opre.37.3.501
[19] Stone, L. D., Theory of Optimal Search (1989), Arlington: Operations Research Society of America, ORSA Books, Arlington
[20] Stromquist, W. R.; Stone, L. D., Constrained optimization of functionals with search theory applications, Mathematics of Operations Research, 6, 4, 518-527 (1981) · Zbl 0511.90087 · doi:10.1287/moor.6.4.518
[21] Washburn, A. R., Search for a moving target, The FAB algorithm, Operations Research, 31, 4, 739-751 (1983) · Zbl 0521.90063 · doi:10.1287/opre.31.4.739
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.